I once asked the question about whether someone had ever played the same numbers and won a bigger share of the jackpot. There were a couple of ‘yes’ answers in that thread.
If you don’t want to flee the country, I think to maximize your take, immediately rent an apartment in a state where there are no state income taxes and the lottery winner can remain anonymous, and buy your ticket(s) there. I don’t know if that combination exists, though. It wouldn’t surprise me in the least if every state that allows winners to remain anonymous also has a state income tax.
I think you’ll want to remain anonymous if at all possible. This will reduce your post-win security costs.
Definitely buy at least two winning tickets, for reasons mentioned upthread. I think I could plausibly get away with buying three jackpot winners without suspicion if I go to different stores and buy multiple tickets at each store, and along the way buy multiple duplicate non-winners too. Some of those non-jackpot winners could net a tiny bit more (relatively) by being winners that match all but the Powerball or some lesser combination. That would increase plausibility; you could say “I had a hunch that five of these would be right but I wasn’t sure about the sixth so I covered my bases!”
While typing this, it occurred to me that there would be some kind of investigation of the winner that “just happened” to buy multiple winning tickets. The chances that the winner’s name would be leaked to the press increases dramatically, blowing the anonymity benefit.